Question

Radius of the curved road on national highway is R. Width of the road is b. The outer edge of the road is raised by h with respect to inner edge so that a car with velocity v can pass safe over it. The value of h is

• A. $\frac{v^{2}b}{Rg}$
• B. $\frac{v}{Rgb}$
• C. $\frac{v^{2}R}{g}$
• D. $\frac{v^{2}b}{R}$

Answer 1

The correct option is A $\frac{v^{2}b}{Rg}$

In equilibrium, $Nsin\theta =\frac{m{v}^2}{R}$ (centripetal force) and $Ncos\theta =mg$

Thus, $tan\theta =\frac{v^2}{Rg}andtan\theta =\frac{h}{b}$

$Hence\frac{h}{b}=\frac{v^2}{Rg}\Rightarrow h=\frac{v^{2}b}{Rg}$